Intelligent imaging method of moving targets for GEO satellite-based bistatic SAR under similarity constraints

Abstract

The present invention provides a GEO satellite-based bistatic SAR moving target intelligent imaging method under similarity constraints, including: collecting echo data containing moving targets through a GEO SA-BSAR system, and performing distance compression, azimuth dimension FFT and clutter suppression processing on the echo data to obtain the range-Doppler domain signal of the moving target; performing distance dimension FFT processing, phase compensation and 2D-IFFT processing on the range-Doppler domain signal to obtain the moving target defocus signal; constructing a deep neural network model based on similarity constraints, the network structure of the deep neural network model is built by a number of residual blocks, and the deep neural network is trained by optimizing the loss function containing similarity measurement to obtain the deep neural network model parameters; the moving target defocus signal is input into the trained deep neural network model, and the focused moving target image is output. The present invention can image the moving target quickly and accurately.

Description

Technical Field

[0001] The present invention relates to the technical field of synthetic aperture radar, and in particular to an intelligent imaging method for moving targets of GEO satellite-airborne bistatic SAR under similarity constraints. Background Art

[0002] The Geosynchronous Spaceborne-Airborne Bistatic Synthetic Aperture Radar (GEO SA-BSAR) uses GEO SAR (Geosynchronous Synthetic Aperture Radar) as a radiation source, and an airborne radar receives signals. It has good concealment and anti-jamming performance, and is flexible in configuration. It is an effective means for detecting and monitoring moving targets.

[0003] The high-altitude transmitting and low-altitude receiving bistatic configuration of GEO SA-BSAR makes the relative motion between the moving target and the radar system more complex, which in turn causes additional phase modulation of the echo signal, resulting in defocusing of the moving target. The traditional GEO SA-BSAR moving target refocusing method requires iterative estimation of target motion parameters, with a large amount of calculation. In recent years, due to pre-learning the mapping relationship between input and output from large-scale data, the deep neural network (DNN) has shown great potential in signal rapid recovery, which inspires us to use it to replace the cumbersome parameter iteration process to improve the imaging ability of moving targets of GEO SA-BSAR.

[0004] Currently, for the SAR moving target imaging method based on the deep neural network, first, signal processing technology is used for clutter suppression and rough imaging of moving targets to obtain a defocused moving target image. Then, the defocused signal is input into the deep neural network to further extract feature information and construct the mapping between the defocused signal and the focused image, and finally, moving target imaging is realized.

[0005] During the moving target imaging process, the moving target image is characterized as the result of focusing of several scattering points. Therefore, the moving target imaging result has the characteristic of sparsity. For the existing SAR moving target imaging method based on the deep neural network, when training the network model, the mean square error is used as the loss function, which is the average error between the predicted image and the reference image, and cannot directly represent the position and focusing characteristics of sparse scattering points. Therefore, it reduces the recovery ability of the network for sparse targets, resulting in the problems of target defocusing and difficult accurate recovery of the scattering point positions, and cannot achieve rapid and high-quality imaging of moving targets. Summary of the Invention

[0006] Based on this, it is necessary to provide an intelligent imaging method for moving targets of GEO satellite-airborne bistatic SAR under similarity constraints in view of the above technical problems.

[0007] An intelligent imaging method for moving targets of GEO satellite-airborne bistatic SAR under similarity constraints includes the following steps:

[0008] Collect echo data containing moving targets through the GEO SA-BSAR system, and perform range compression, azimuth FFT, and clutter suppression processing on the echo data to obtain the range-Doppler domain signal of the moving target, including:

[0009] Collect echo data containing moving targets through the GEO SA-BSAR system, and perform range compression on the echo data to obtain the first signal as:

[0010]

[0011] where r is the range, t a is the slow time, c is the speed of light, σ t,k and R t,k (t a ) are respectively the scattering coefficient and the two-way slant range history of the k-th scatterer, λ is the wavelength, c(r,t a ) is the stationary clutter signal, and n(r,t a ) is the noise;

[0012] Transform the first signal to the range-Doppler domain through azimuth FFT to obtain the second signal as:

[0013]

[0014] where f a is the azimuth frequency, W a,k (f a ) and ψ k (f a ) are respectively the slant range frequency domain expression, azimuth envelope, and range-Doppler domain signal phase of the k-th scatterer; c(r,f a ) and n(r,f a ) are respectively the range-Doppler domain signals of clutter and noise;

[0015] Suppress clutter for the second signal through Doppler filtering or space-time adaptive processing method to obtain the range-Doppler domain signal as:

[0016]

[0017] Perform range - dimension FFT processing, phase compensation, and 2D - IFFT processing on the range - Doppler domain signal to obtain the defocused signal of the moving target, including:

[0018] Perform range - dimension FFT processing on the range - Doppler domain signal to obtain a two - dimensional frequency - domain signal, expressed as:

[0019]

[0020] where f r is the range frequency, W k (f r , f a ) and are respectively the two - dimensional frequency - domain signal envelope and phase of the k - th scatterer. Among them, the two - dimensional frequency - domain signal phase of the k - th scatterer is approximately:

[0021]

[0022] where R 0,k , k 1,k , k 2,k , k 3,k and k 4,k are respectively the constant term, the first - to - fourth - order term coefficients after the Taylor expansion of the round - trip slant - range history R t,k (t a ) with respect to the slow time t a ; f 0 is the radar operating frequency;

[0023] Perform phase compensation and 2D - IFFT processing on the two - dimensional frequency - domain signal to obtain the defocused signal of the moving target, that is:

[0024] s de (r, t a ) = IFFT 2D [s t,f (f r , f a)h com (f r , f a )];

[0025] where IFFT 2D [s t,f (f r , f a )h com (f r , f a )] represents 2D - IFFT processing, and the compensation reference function h com (f r , f a) is constructed based on the high-order phase of the two-dimensional spectrum of the center point signal of the static scene, and its expression is:

[0026]

[0027] where k 10 、k 20 、k 30 and k 40 are respectively the coefficients of the first to fourth order terms after the two-way slant range history of the center point of the static scene is expanded by Taylor series with respect to slow time;

[0028] Construct a deep neural network model based on similarity constraints. The network structure of the deep neural network model is built by several residual blocks, and the deep neural network is trained by optimizing the loss function containing similarity metrics to obtain the parameters of the deep neural network model. The loss function is:

[0029]

[0030] where I is the input data, O is the label data, C(I) is the processing result of the deep neural network model based on similarity constraints, and [C(I)] xy represents the pixel value of C(I) at the (x, y) position, O xy represents the pixel value of O at the (x, y) position, N a is the number of azimuth points of the signal, and N r is the number of range points of the signal;

[0031] Input the defocused signal of the moving target into the trained deep neural network model, and output the focused moving target image.

[0032] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows: The present invention collects echo data containing moving targets through the GEO SA-BSAR system, performs range compression, azimuth FFT, and clutter suppression processing on the echo data to obtain the range-Doppler domain signal of the moving target, performs range FFT processing, phase compensation, and 2D-IFFT processing on the range-Doppler domain signal to obtain the defocused signal of the moving target; constructs a deep neural network model based on similarity constraints, and the network structure of the deep neural network model is built by several residual blocks, which improves the expression ability of the network, realizes the imaging of moving targets under different bistatic configurations, and trains the deep neural network by optimizing the loss function containing similarity metrics to obtain the deep neural network model parameters. Input the defocused signal of the moving target into the trained deep neural network model to obtain a focused moving target image, which can quickly and accurately image the moving target; by introducing the cosine similarity metric of the azimuth signal into the loss function, the learning of the sparse target position and focusing features in the training image by the network structure is strengthened, so as to obtain better moving target imaging results with less training data. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a schematic flow chart of an intelligent imaging method for moving targets of GEO satellite-borne bistatic SAR under similarity constraints in an embodiment;

[0034] Figure 2 It is the intelligent imaging results of moving targets of GEO satellite-borne bistatic SAR obtained by the proposed network of the present invention under different signal-to-noise ratios. Among them, (a) is a defocused image without noise; (b) is a defocused image with a signal-to-noise ratio of 5 dB; (c) is a defocused image with a signal-to-noise ratio of 10 dB; (d) is a reference image; (e) is a network prediction image without noise; (f) is a network prediction image with a signal-to-noise ratio of 5 dB; (g) is a network prediction image with a signal-to-noise ratio of 10 dB;

[0035] Figure 3 It is the intelligent imaging results of moving targets of GEO satellite-borne bistatic SAR obtained by the proposed network of the present invention under different bistatic configurations. Among them, (a) is a defocused image of the target with the aircraft looking forward; (b) is a defocused image of the target with the aircraft looking sideward; (c) is a defocused image of the target with the aircraft looking backward; (d) is a reference image with the aircraft looking forward; (e) is a reference image with the aircraft looking sideward; (f) is a reference image with the aircraft looking backward; (g) is a network prediction image with the aircraft looking forward; (h) is a network prediction image with the aircraft looking forward; (i) is a network prediction image with the aircraft looking forward;

[0036] Figure 4 It is the network recovery performance of the present invention under different signal-to-noise ratios and bistatic configurations. Among them, (a) is 3000 groups of training data; (b) is 1000 groups of training data;

[0037] Figure 5 For the scattering point position recovery performance of the present invention under different signal-to-noise ratios and bistatic configurations, where (a) is the azimuth position mean square error; (b) is the range position mean square error. Specific embodiments

[0038] In order to make the objectives, technical solutions and advantages of the present invention clearer, the following further details the present invention through specific embodiments in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0039] In one embodiment, as Figure 1 shown, a GEO satellite-borne bistatic SAR moving target intelligent imaging method under similarity constraints is provided, including the following steps:

[0040] Step S101, collect echo data containing moving targets through a GEO SA-BSAR system, and perform range compression, azimuth FFT, and clutter suppression processing on the echo data to obtain the range-Doppler domain signal of the moving target.

[0041] Specifically, collect echo data containing moving targets through a geosynchronous orbit satellite-borne bistatic synthetic aperture radar system, i.e., a GEO SA-BSAR system, and perform range compression on the collected echo data so that the position of the moving target conforms to the change of the radar range (instantaneous slant range); secondly, perform azimuth FFT (fast Fourier transform) processing on the compressed echo data for subsequent operations; finally, since there are unwanted reflectors in the echo data, i.e., clutter, which will interfere with the normal operation of the radar, it is necessary to perform clutter suppression on the echo data to obtain a more accurate range-Doppler domain signal of the moving target.

[0042] Among them, when performing clutter suppression processing, methods such as Doppler filtering or space-time adaptive processing can be used.

[0043] Specifically, collect echo data containing moving targets through a GEO SA-BSAR system, and perform range compression on the echo data to obtain the first signal as:

[0044]

[0045] where r is the range, t a is the slow time, c is the speed of light, σ t,k and R t,k (t a ) are respectively the scattering coefficient and the two-way slant range history of the kth scattering point, λ is the wavelength, c(r,ta ) is the stationary clutter signal, n(r,t a ) is the noise;

[0046] The first signal is transformed to the range-Doppler domain through azimuth dimension FFT to obtain the second signal as:

[0047]

[0048] where f a is the azimuth frequency, W a,k (f a ) and ψ k (f a ) are respectively the slant range frequency domain expression, azimuth envelope and range-Doppler domain signal phase of the k-th scatterer; c(r,f a ) and n(r,f a ) are respectively the range-Doppler domain signals of clutter and noise;

[0049] The second signal is subjected to clutter suppression through Doppler filtering or space-time adaptive processing method to obtain the range-Doppler domain signal as:

[0050]

[0051] where, W a,k (f a ) and ψ k (f a ) are respectively the slant range frequency domain expression, azimuth envelope and range-Doppler domain signal phase of the k-th scatterer, n(r,f a ) is the range-Doppler domain signal of noise.

[0052] Step S102, perform range dimension FFT processing, phase compensation and 2D-IFFT processing on the range-Doppler domain signal to obtain the defocused signal of the moving target.

[0053] Specifically, perform range dimension FFT processing on the obtained range-Doppler domain signal to obtain a two-dimensional frequency domain signal; perform phase compensation on the two-dimensional frequency domain signal to initially compensate the phase of the signal in the frequency domain, so that the time domain signals of the moving targets are coherently superimposed and the signal-to-noise ratio is improved; finally, perform 2D-IFFT (2D-Inverse Fast Fourier Transform) processing on this signal to obtain the defocused signal of the moving target.

[0054] Among them, when performing phase compensation, the reference function for phase compensation is constructed using the high-order phase of the two-dimensional spectrum of the stationary center point signal.

[0055] Specifically, perform range - dimension FFT processing on the range - Doppler domain signal to obtain a two - dimensional frequency domain signal, expressed as:

[0056]

[0057] where f r is the range frequency, W k (f r , f a ) and are respectively the two - dimensional frequency domain signal envelope and phase of the k - th scatterer. Among them, the two - dimensional frequency domain signal phase of the k - th scatterer can be approximated as:

[0058]

[0059] where R 0,k , k 1,k , k 2,k , k 3,k and k 4,k are respectively the constant term, the first - to - fourth - order term coefficients after the Taylor expansion of the two - way slant - range history R t,k (t a ) with respect to the slow time t a ; f 0 is the radar operating frequency;

[0060] Perform phase compensation and 2D - IFFT processing on the two - dimensional frequency domain signal to obtain the defocused signal of the moving target, that is:

[0061] s de (r, t a ) = IFFT 2D [s t,f (f r , f a )h com (f r , f a )];

[0062] where IFFT 2D [s t,f (f r , f a )h com (f r , f a )] represents 2D - IFFT processing, and the compensation reference function h com (f r , f a ) is constructed based on the high - order phase of the two - dimensional spectrum of the signal at the center point of the stationary scene, and its expression is:

[0063]

[0064] Among them, k 10 , k 20 , k 30 and k 40 are respectively the first to fourth order term coefficients after the two-way slant range history of the center point of the static scene is expanded by Taylor series with respect to slow time.

[0065] Step S103: Construct a deep neural network model based on similarity constraints. The network structure of the deep neural network model is built by several residual blocks, and the deep neural network is trained by optimizing the loss function containing similarity measurement to obtain the deep neural network model parameters.

[0066] Specifically, a deep neural network model is constructed based on similarity constraints. Multiple training images are collected as the training set and the validation set. The deep neural network model is trained with the training set and verified with the validation set. At the same time, the loss function containing similarity measurement is used to strengthen the learning of the sparse target position and focused features in the training images by the deep neural network model during the training process, so that the trained deep neural network model can obtain higher-quality moving target imaging results with fewer training images.

[0067] Among them, the use of residual blocks can construct a deeper network structure, thereby improving the network expression ability and realizing moving target imaging under different bistatic configurations.

[0068] Among them, the loss function is:

[0069]

[0070] Among them, I is the input data, O is the label data, C(I) is the processing result of the deep neural network model based on similarity constraints, and [C(I)] xy represents the pixel value of C(I) at the (x, y) position, O xy represents the pixel value of O at the (x, y) position, N a is the number of azimuth points of the signal, and N r is the number of range points of the signal.

[0071] Specifically, the cosine similarity of the azimuth signal is introduced in the above loss function, which can strengthen the learning of the sparse target position and focused features in the training images by the deep neural network model, and is convenient for obtaining better moving target imaging results with less training data.

[0072] Step S104: Input the defocused signal of the moving target into the trained deep neural network model, and output the focused moving target image.

[0073] Specifically, the obtained defocused signal of the moving target is input into the trained deep neural network model. The deep neural network model processes the defocused signal of the moving target and outputs a focused image of the moving target, solving the problem that the moving target is defocused and the positions of the scattering points cannot be accurately restored, and enabling the rapid and accurate acquisition of the focused image of the moving target.

[0074] In this embodiment, the echo data containing the moving target is collected by the GEO SA - BSAR system, and the echo data is subjected to range compression, azimuth - dimension FFT, and clutter suppression processing to obtain the range - Doppler domain signal of the moving target. The range - Doppler domain signal is subjected to range - dimension FFT processing, phase compensation, and 2D - IFFT processing to obtain the defocused signal of the moving target. A deep neural network model is constructed based on similarity constraints. The network structure of the deep neural network model is built by several residual blocks, which improves the expression ability of the network, realizes the imaging of moving targets under different bistatic configurations, and the deep neural network is trained by optimizing the loss function containing similarity metrics to obtain the parameters of the deep neural network model. The defocused signal of the moving target is input into the trained deep neural network model to obtain a focused image of the moving target, enabling the rapid and accurate imaging of the moving target. By introducing the cosine similarity metric of the azimuth - direction signal into the loss function, the learning of the sparse target positions and focused features in the training images by the network structure is strengthened, so as to obtain better moving target imaging results with less training data.

[0075] To obtain an achievable GEO SA - BSAR moving target imaging network model, a large amount of simulation data is required to pre - train the model parameters. When generating training data, the bistatic configuration parameters of GEO SA - BSAR need to be randomly set. These parameters include the aircraft incident angle, bistatic angle, and platform velocity angle to obtain the echo signals of the scattering points under different bistatic configurations. Among them, the number of targets, the scattering coefficients of each target, the target point positions, the target velocities, and accelerations are also randomly set. The parameter variation ranges are shown in Table 1. Then, through range compression, 2D - FFT processing, phase compensation, and 2D - IFFT processing, a defocused image of the moving target is obtained.

[0076] Table 1 Parameters and variation ranges randomly changed during simulation training data

[0077] Parameter Random variation range Parameter Random variation range Aircraft incident angle (0, π / 2) rad Ground projection of bistatic angle [0, 2π) rad Ground projection of velocity angle [0, 2π) rad True anomaly of GEO satellite [0, 2π) rad Aircraft speed [80, 200] m / s Target speed ±[1, 18] m / s Target acceleration <![CDATA[[-0.1,0.1]m / s 2 > Signal-to-noise ratio [5, 10] dB Number of azimuth points × Number of range points 512×128 Number of targets {1,2,3,4,5,6,7,8,9,10}

[0078] Considering the influence of noise, noise with a signal-to-noise ratio (SNR) ranging from 5 to 10 dB can be randomly generated. The corresponding reference image is obtained by convolving the target scattering coefficient with a Gaussian function, and the width of the Gaussian function is set to 1 pixel unit. Through the above steps, a training data pair containing the input and reference images is obtained. Since the defocused image is complex data, the real and imaginary parts of the defocused image are respectively input into the network as two channels, and the output is a one-channel target amplitude map.

[0079] Since not all GEO SA-BSARs in bistatic configurations are suitable for imaging, when generating training data, training data with an azimuth bandwidth less than 6.5 Hz can be extracted to avoid deterioration of the model training results by simulation data that does not have two-dimensional resolution capabilities.

[0080] In one embodiment, the training data can be 3000 groups, and the Adam solver is used during the training process; the learning rate decays exponentially, with an initial value of 10 -4 , and it becomes one-tenth of the initial value every 50 epochs. The Batchsize is set to 32.

[0081] The defocused images of moving targets with different SNRs are input into the trained network, and the input images and predicted images are as Figure 2 shown. Under different SNR conditions, the network can obtain focused imaging results of moving targets, and as the SNR of the input data increases, the network has better output results.

[0082] In one embodiment, to evaluate the prediction performance of the trained DNN network model based on similarity constraints under different bistatic configurations, the input SNR is set to 10 dB, and the defocused moving targets generated under different bistatic configurations are input into the trained network. The input images and predicted images obtained are as Figure 3 shown. It can be seen that regardless of whether the airborne platform is in the forward-looking, side-looking, or rear-looking situation, the network can obtain good imaging results of moving targets.

[0083] To discuss the superiority of the modified loss function, the performance of the network model using the mean square error (MSE) as the loss function in this embodiment is compared with the network model of the present invention, as Figures 4 to 5 shown.

[0084] To analyze the network performance under different SNRs, 1000 Monte Carlo simulations are performed on the network under different SNRs. Figure 4Among them, (a) shows the image restoration performance of the network obtained based on 3,000 groups of training data. It can be seen that when the signal-to-noise ratio is relatively high, the MSE of the network is lower, indicating better restoration performance, and there is no significant difference in the image restoration performance among different bistatic configurations. For the network model of the present invention, when the signal-to-noise ratio is greater than 0 dB, the MSE tends to be stable. However, for the network with MSE as the loss function, its MSE does not decrease significantly until the signal-to-noise ratio is greater than 5 dB. Therefore, the network trained with the proposed loss function has better image restoration ability than the network trained with MSE as the loss function under low signal-to-noise ratio conditions.

[0085] In addition, the network can also obtain good performance when the training data is less. When there are only 1,000 groups of training data, the network performance results are as Figure 4 shown in (b). For the proposed network model, the network trained with 1,000 groups of data can obtain almost the same image restoration performance as the network trained with 3,000 groups of data. However, the performance of the network with MSE as the loss function is worse than that of the proposed network model, indicating the superiority of the network of the present application when the training data is less.

[0086] Due to the addition of the cosine similarity of the azimuth signal in the loss function, compared with the network with MSE as the loss function, the position error of the scattering points of the proposed network is smaller, as Figure 5 shown. Figure 5 In (a) and (b) of it are the position errors of the scattering points in the azimuth and range directions respectively. When the signal-to-noise ratio is between 0 dB and 20 dB, under different bistatic configurations, the position errors of the scattering points obtained by the proposed network have no significant difference, the MSE of the azimuth position is less than 3, and the position MSE of the range direction is less than 0.2. For the network with MSE as the loss function, its position error is larger, especially when the signal-to-noise ratio is not in the range of 5 to 10 dB. Therefore, the proposed network has good generalization ability.

[0087] The implementation results show that by introducing the cosine similarity of the azimuth signal into the loss function, the learning of the position and focusing characteristics of moving targets in the training images by the network can be strengthened, and this moving target imaging method can obtain better moving target imaging results with less training data.

[0088] By using the mean square error of the above input and output data and the cosine similarity of the azimuth signal as the loss function together, it can be known that the present application can improve the learning of the sparse target characteristics by the network during the training process, so that the network can obtain a network model with better generalization ability on a small training set.

[0089] The above content is a further detailed description of the present invention in combination with specific implementation manners. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, and all should be regarded as falling within the protection scope of the present invention.

Claims

1. A GEO satellite-based bistatic SAR moving target intelligent imaging method under similarity constraints, characterized in that: The following steps are involved: The GEO SA-BSAR system collects echo data containing moving targets, performs range compression, azimuth FFT and clutter suppression on the echo data, and obtains the range-Doppler domain signal of the moving target, including: The GEO SA-BSAR system collects echo data containing moving targets and performs distance compression on the echo data to obtain the first signal: Where r is the distance, t a is the slow time, c is the speed of light, σ t,k and R t,k (t a ) are the scattering coefficient and two-way slant range of the kth scattering point, λ is the wavelength, c(r,t a ) is a stationary clutter signal, n(r,t a ) is noise; The first signal is transformed into the range-Doppler domain through azimuth FFT to obtain the second signal: Among them, f a is the azimuth frequency, W a,k (f a ) and ψ k (f a ) are the slant range frequency domain expression, azimuth envelope and range-Doppler domain signal phase of the kth scattering point respectively; c(r,f a ) and n(r,f a ) are the range-Doppler domain signals of clutter and noise respectively; The second signal is subjected to clutter suppression by Doppler filtering or space-time adaptive processing method to obtain a range-Doppler domain signal: Performing range-dimensional FFT processing, phase compensation and 2D-IFFT processing on the range-Doppler domain signal to obtain a moving target defocus signal, including: The range-Doppler domain signal is subjected to range-dimensional FFT processing to obtain a two-dimensional frequency domain signal, which is expressed as: Among them, f r is the distance frequency, W k (f r ,f a )and are respectively the two-dimensional frequency domain signal envelope and phase of the k-th scattering point, where the two-dimensional frequency domain signal phase of the k-th scattering point is approximately: Among them, R 0,k , k 1,k , k 2,k , k 3,k and k 4,k are the two-way slant range history R of the kth scattering point t,k (t a ) for slow time t a The constant term and the coefficients of the first to fourth order terms after Taylor expansion; f0 is the radar operating frequency; Phase compensation and 2D-IFFT processing are performed on the two-dimensional frequency domain signal to obtain a moving target defocus signal, namely: s de (r,t a )=IFFT 2D [s t,f (f r ,f a )h com (f r ,f a )]; Among them, IFFT 2D [s t,f (f r ,f a )h com (f r ,f a )] represents 2D-IFFT processing, the reference function h of compensation com (f r ,f a ) is constructed based on the high-order phase of the two-dimensional spectrum of the center point signal of the static scene, and its expression is: Among them, k 10 , k 20 , k 30 and k 40 They are the first to fourth order coefficients of the Taylor expansion of the two-way slant range history of the center point of the stationary scene for the slow time; A deep neural network model based on similarity constraints is constructed. The network structure of the deep neural network model is built by several residual blocks, and the deep neural network is trained by optimizing the loss function containing similarity measurement to obtain the deep neural network model parameters. The loss function is: Where I is the input data, O is the label data, C(I) is the processing result of the deep neural network model based on similarity constraints, [C(I)] xy represents the pixel value of C(I) at position (x, y), O xy represents the pixel value of O at position (x, y), N a is the number of signal azimuth points, N r is the distance point number of the signal; The moving target defocus signal is input into a trained deep neural network model, and a focused moving target image is output.

Images